re: Italy (Rome/Florence/Venice) eating recommendations?

Trastevere is a great neighborhood. I like Pizzeria Ai Marmi, on viale Trastevere. If you go early, right when it opens, you won't have to wait for a table. Super thin crust Roman pizza, braised artichokes, suppli (arancini, or fried rice balls stuffed with cheese), plus simple stuff like crostini topped with beans, etc. Outside of Trastevere, seek out the food shops Volpetti, Castroni, and the Roscioli bakery on via del Gubbionari for a porchetta sandwich.

If you are intrepid, you can take the train from FCO to the Trastevere station for less than 15 euro. It is an easy way to get into town without fighting traffic.

ETA in Florence, Fabiola Picchis celebrated ristorante Cibreo shares a kitchen with his trattoria Cibreo, so you can sample his Tuscan cuisine at a lower pricing point with no reservations.